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Is there a specific reason you want BofA? I remember being approved in the up mid 600's for a BOA card, but if your scores are really mid 600 I think Capital One might be a better choice if you're looking for a higher limit and an introductory lower APR. Capital One cards definititevly grow at least a little, if not a lot. The only real con I can think of compared to BOA is that Capital One is a triple pull.
That being said, my BOA cards generally have the lowest actual APR.
I don't think you should put all your eggs in Bank of America's basket as far as which CRA they pull. I apped with them a few months ago and they pulled Exp and Trans. Perhaps others could offer more advice, but I'd be wary of investing much into your current idea. For example, you may apply and be approved at BOA only to be hit with a 500$ limit, which probably wouldn't be very useful for a balance transfer. It's hard to make any useful financial planning when you're relying on a plan with so many variables. You said you have an auto loan with Wells Fargo thats in good standing, would it be possible to consider a personal loan instead of a credit card if a lower APR is what you're moslty interested in?
Hope it helps.
Scores are only one part of the equation. What is causing yours to be low?
definitely want to wait for scores to update with low utilization if you are at all iffy on being approved for a new app. I was reminded of this just this week after applying for what I thought would be a SP CLI from US Bank... completely forgot that I am waiting for ~ 5k CLIs and -1800 balance to report... whoops! live and learn.